# Graphing Equations

Math
• Study Guide
Summary

## Graphing Equations Using a Data Table

Summary Graphing Equations Using a Data Table

One of the main uses of an xy-graph is to graph equations. If an equation has both an x and y variable, then it often has multiple solutions of the form (x, y). In fact, there are generally infinitely many solutions to an equation with two variables.

The solutions to an equation in two variables can be represented by a curve on an xy-graph; every point on the curve has coordinates which satisfy the equation. In fact, for linear equations (our only concern in this chapter), the curve representing the solutions to the equation will actually be a straight line.

Example. Here is the graph of 2y - x = 4: Graph of 2y - x = 4 If we pick any point on the line -- (2, 1), (- 4, 0), or ( , 2 ), for example -- it will satisfy the equation 2y - x = 4. Try a few points; they need not have integer values.

### Making Data Tables

One way to graph an equation is by use of a data table. A data table is a list of x-values and their corresponding y-values. To make a data table, draw two columns. Label one column x and the other column y. Then list the x-values -2, - 1, 0, 1, 2 in the x column:

Next, plug each value of x into the equation and solve for y. Insert these values of y into the table, under their corresponding x values. For this example, we will use the equation 2x - 4 = 3y:
x = - 2: 2(- 2) - 4 = 3y. 3y = - 8. y = - 2 x = - 1: 2(- 1) - 4 = 3y. 3y = - 6. y = - 2
x = 0: 2(0) - 4 = 3y. 3y = - 4. y = - 1 x = 1: 2(1) - 4 = 3y. 3y = - 2. y = - x = 2: 2(2) - 4 = 3y. 3y = 0. y = 0
Thus, the data table looks like: